How do you divide #(x^4-2x^2+10)/(x-1)# using long division? What is the quotient and remainder?

1 Answer
maganbhai P.
Aug 13, 2018

#Quotient :q(x)=x^3+x^2-x-1# #"and Remainder " :r(x)=9#

Explanation:

Here ,

Dividend #:color(blue)(x^4+0x^3-2x^2+0x+10 and# divisor #: color(red)(x-1)#

So ,
#color(white)(..............................)ul(x^3+x^2-x-1color(white)(.........))larrquotient#
#color(white)(..................)(x-1) # #|# #x^4+0x^3-2x^2+0x+10#

#color(white)(......)color(violet)((x-1)*x^3tocolor(white)(......)ul(x^4-x^3)##color(white)(.......)lArr"subtract"#
#color(white)(........................................0)x^3-2x^2#

#color(white)(..........)color(violet)((x-1)*x^2tocolor(white)(.......)ul(x^3-x^2)##color(white)(.......)lArr"subtract"#
#color(white)(...............................................)-x^2+0x#

#color(white)(.......................)color(violet)((x-1)(-x))color(white)(......)ul(-x^2+x)color(white)(.......)lArr"subtract"#
#color(white)(.......................................................)-x+10#

#color(white)(.................color(violet)((x-1)(-1))...................)ul(-x+1)color(white)(...)lArr"subtract"#

#color(white)(...................................................................)9larr"Remainder"#

Hence ,

#(color(blue)(x^4+0x^3-2x^2+0x+10))=(x-1)(x^3+x^2-x-1)+9#

#Quotient :q(x)=x^3+x^2-x-1# #"and Remainder " :r(x)=9#

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